This paper proposed a novel, efficient method to estimate challenging small structural motions from noisy video. To eliminate the phase limitation, ill-posed problem, and high computational burden, the structural motion function is resampled and recovered. Because video signals have tremendous redundancies in spatial, block, and time domains, the objective is achieved by enforcing three levels of sparsity constraints. In the first step, the ill-posed optimization is solved using the multi-hypothesis prediction embedded with the Tikhonov regularization, to resample and recover the video signal in the spatial domain. The second step is to characterize the measurement uncertainty in the block domain, in which two weight matrices are proposed into the regularization terms of the sparse coding. Finally, the temporal correlation of video frames is exploited by the reweighted residual sparsity. The superiority of the sparsity-enforcement method over existing methods was demonstrated through several case studies. Among the comparisons, the sparsity-enforcement method yielded video magnifications, structural motions, and modal information more accurately. Meanwhile, it has the lowest computational burden.

中文翻译：

---

基于稀疏执行估计小结构运动

本文提出了一种新颖、有效的方法来估计嘈杂视频中具有挑战性的小结构运动。为了消除相位限制、不适定问题和高计算负担，对结构运动函数进行了重新采样和恢复。由于视频信号在空间、块和时间域中具有巨大的冗余，因此通过实施三个级别的稀疏性约束来实现该目标。在第一步中，使用嵌入了 Tikhonov 正则化的多假设预测来解决病态优化，以在空间域中重新采样和恢复视频信号。第二步是表征块域中的测量不确定性，其中将两个权重矩阵提出到稀疏编码的正则化项中。最后，重新加权的残差稀疏性利用了视频帧的时间相关性。通过几个案例研究证明了稀疏性执行方法优于现有方法的优越性。在比较中，稀疏性执行方法更准确地产生了视频放大、结构运动和模态信息。同时，它的计算负担最低。